Research Article Modeling Large Deformation and Failure of ...downloads.hindawi.com/journals/mse/2014/292647.pdf · LS-Dyna provides many material models for di erent types of foams

Research ArticleModeling Large Deformation and Failure of ExpandedPolystyrene Crushable Foam Using LS-DYNA

Qasim H. Shah and A. Topa

Department of Mechanical Engineering, Faculty of Engineering, International Islamic University Malaysia, 53100 Jalan Gombak,Kuala Lumpur, Malaysia

Correspondence should be addressed to Qasim H. Shah; [email protected]

Received 31 May 2013; Accepted 31 October 2013; Published 27 January 2014

Academic Editor: Dimitrios E. Manolakos

Copyright © 2014 Q. H. Shah and A. Topa. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.

In the initial phase of the researchwork, quasistatic compression tests were conducted on the expanded polystyrene (EPS) crushablefoam formaterial characterisation at low strain rates (8.3×10−3 ∼ 8.3×10−2 s−1) to obtain the stress strain curves.The resulting stressstrain curves are compared well with the ones found in the literature. Numerical analysis of compression tests was carried out tovalidate them against experimental results. Additionally gravity-driven drop tests were carried out using a long rod projectile withsemispherical end that penetrated into the EPS foam block. Long rod projectile drop tests were simulated in LS-DYNA by usingsuggested parameter enhancements that were able to compute the material damage and failure response precisely. The materialparameters adjustment for successful modelling has been reported.

1. Introduction

Crushable foams are suitable solution in the field of shockmitigation and impact absorption applications because oftheir incombustibility, cost, complex compression behavior,and high energy absorption capabilities [1]. In safety appli-cations, accurate predictions of behaviour of shock absorbermaterials are extremely important because the experimentalwork is a resource hungry process.

Throughout the past years, the range of applications ofcrushable foams has become wider and larger as engineersand designers keep altering the microstructure of the foammaterials in order to achieve the desired mechanical proper-ties and behaviour that fulfil the requirements regarding theirapplications. Crushable foams aremainly used in cushioning,impact mitigation, energy absorption, and comfort applica-tions [2].

One way to increase the car body stiffness and crash-worthiness is the utilization of local reinforcements with syn-thesized polyurethane foam. The crushable foams have sev-eral advantages over other reinforcement materials becauseof their high energy absorbing capabilities, coupledwith theirlow cost and weight [3].

Another important application of the crushable foamsis the aircraft runway arrestor systems. The aircraft mightoverrun the available runway area during take-off or landing.Crushable foam arrestor bed systems mitigate the overrunwhich prevents accidents involving aircraft damage and lossof life [4].

In automotive safety, the crushable foams are used in thenew Steel And Foam Energy Reducing (SAFER) barriers.In many NASCAR racetracks, simple crushable polystyreneinsulation foam blocks are placed between the outer steeltube, and the inner concrete wall. This SAFER barrier is verylow in cost and weight and easy to fabricate [5, 6].

Another application for the crushable foams is in oil wellcasing. Heat is generated due to the normal drilling andproduction applications. As temperature rises, the trappedfluids tend to expand and potentially can create a veryhigh pressure. The most effective mitigation solution for thispressure build-up is the application of crushable foam wrap.This will allow the fluid trapped within the casing annulusto expand. The crushable foam wrap is predetermined tocollapse before any potential dangerous pressure may exist[7].

Hindawi Publishing CorporationModelling and Simulation in EngineeringVolume 2014, Article ID 292647, 7 pageshttp://dx.doi.org/10.1155/2014/292647

2 Modelling and Simulation in Engineering

Extensive experimental work has been conductedto determine the mechanical properties of expandedpolystyrene foams. Difficulties arise in modelling these typesof materials because they are stain rate dependant. Previousstudies show that the rate dependant behaviour is linear withthe logarithm of the strain rate [2]. Moreover, the mechanicalproperties of polymeric foams depend on their density [8, 9].Therefore, developing the material model depends on thedensity of the foams and their applications.

The complexity of the mechanical behaviour of thecrushable foams is a consequence of its cellular structure.Compression is the most common mode of deformationfor crushable foams as they are weak in tension and shear.However, tension and shear deformation can occur due toconcentrated compressive loads or the geometry of crushablefoams [2].

In pure compression, there are three regions in the stress-strain relationship: linear compression, stress plateau, andnon-linear compression. Poisson’s ratio is negligible in purecompression. In pure tension, thematerial behaves linearly inlow deformation. However, nonlinear behaviour is observedat large deformations [10, 11].

In previous work, material models for EPS foams weredeveloped. These models were proved to be successful inthe cases of uniform compression loading and low velocitylocalized damage [5, 6, 12, 13]. However, during high velocitylocalized compression, the material undergoes a combinedmode of compression and tension. Brittle rupture and crackinitiation are experimentally observed in thematerial [14, 15].Therefore, these material models need to be improved toinclude the brittle failure behaviour.

2. Experimental Work

2.1. QuasiStatic Compression Test. The quasistatic compres-sion tests were conducted on cubic specimens of EPS crush-able foamwith the side length of 100mm.The average densityof the specimen was measured as 12.75 kg/m3. The specimenwas compressed until 80% of its initial length. The compres-sion test was carried out at three different compression rates:50mm/min, 250mm/min, and 500mm/min and the strainrates for these three compression rates were calculated as0.00833/s, 0.04167/s, and 0.0833/s, respectively.

Upon examining the specimen during the compressiontest, no lateral elongation was observed as seen in Figure 1.This proves that EPS crushable foams have zero Poisson’sratio. The volume of the material is not conserved duringcompression. Instead, the density increases while thematerialis compressed. Poisson’s ratio plays an important role in stressstrain diagrams.The initial and final cross section areas of theEPS crushable foams in compression remain constant. Thus,the engineering and true stress strain diagrams are identical.

When the compressive load was removed, the specimenelastically recovered to approximately 50%of its initial length.This is due to the elastic component (matrix material) ofpolymeric foams. However, a permanent damage is observedbecause of the foam cells collapsing in the stress plateauregion.

Figure 1: Quasistatic compression test of EPS crushable foam.

0

0.1

0.2

0.3

0.4

0.5

0.6

0 10 20 30 40 50 60 70 80 90

Stre

ss (M

Pa)

Strain (%)

500mm/min250mm/min50mm/min

Figure 2: Rate dependency of EPS crushable foam.

Table 1: Effects of strain rate on yield stress, Young’s Modulus, andabsorbed energy.

Strain rate Yield stress Young’s Modulus Absorbed energy(s−1) (MPa) (MPa) (J)0.00833 0.020 0.8 104.890.04167 0.035 1.4 118.950.08333 0.055 2.2 135.06

The results of the compression test are plotted in Figure 2.The three regions of deformation are observed in EPScrushable foams. However, the transition point between thestress plateau and densification regions are not clear. Thisis believed to be due to the destruction of foam cells andthe permanent damage. The yield stress, Young’s Modulusand total absorbed energy by the foam material are listed inTable 1.

Modelling and Simulation in Engineering 3

0.6

0.5

0.4

0.3

0.2

0.1

00.60.50.40.30.20.10 0.7 0.8 0.9

Stre

ss (M

Pa)

Strain (mm/mm)

ExperimentLiterature

Figure 3: Comparison between literature data and experimentaldata.

Guide tube

Gui

de tu

be

Foam

Figure 4: Set-up for drop test experiment.

To validate the results of the experiment, the stress straincurve at a strain rate of 0.0833 s−1 was compared to thestress strain curves found in the literature [2]. As observedin Figure 3, there is a slight difference in the two curves. Thisis because of the small difference in the strain rate and thedensity of the material. The specimen in the literature hadslightly higher density and the strain rate was a little larger.

2.2. Gravity-Driven Drop Test. A specimen of EPS crushablefoam having a square base with the side length of 250mmand the height of 400mm was secured to the ground. A650mm long cylinder (3.39 kg) with a diameter of 50mmanda semi-spherical head was dropped on the specimen througha cylinder tube guide. The altitude of the long rod drop was6 meters and the projectile accelerated due to gravity andreached the velocity of 10.85m/s before hitting the specimen.The set up of the experiment is shown in Figure 4. A localizeddamage was observed on the projected area of the projectileand the surrounding surface area of the specimen was not

Hole

FoamPr

ojec

tile

Figure 5: Localized damage on the specimen.

Proj

ectil

e

Com

pres

sed

mat

eria

l

Figure 6: Depth of penetration of projectile into EPS foam speci-men.

affected as seen in Figure 5. This damage was confined to astraight cylindrical hole in the foam specimen. Due to thesmall elastic recovery of the specimen, the projectile bouncedup slightly after reaching themaximum depth of penetration.The damage in the specimen was highlighted as shown inFigure 6. Table 2 summarizes the results of the drop testexperiment.

3. Numerical Simulation

3.1. Compression Test Simulation. The simulation of the quasistatic compression test was successfully performed using LS-Dyna. LS-Dyna provides many material models for differenttypes of foams [16]. However, based on previous work byOzturk and Anlas [12], the best candidate for modeling EPScrushable foam is MAT CRUSHABLE FOAM.This materialmodel required the input of five parameters: density ofmaterial, modulus of elasticity, Poisson’s ratio, stress straincurve, tensile stress cutoff, and damping coefficient. Thefirst four parameters were found experimentally. However,tensile cutoff and viscous damping coefficient were obtained


Table 2: Maximum depth of penetration of the projectile.

DOP (mm)Specimen 1 189Specimen 2 190Specimen 3 186Specimen 4 187Average 188

from the literature [12]. The parameters for the materialmodel are listed in Table 3. The model was finely meshedto obtain accurate results. The lower nodes of the modelwere fixed while the upper nodes were given a prescribedmotion at 500mm/min. The results of the simulation arelisted in Figure 7. A comparison between the simulation andthe experimental results show very small difference and thusverifies the material model developed for compression.

3.2. Drop Test Simulation. Thematerial model developed forthe compression test simulation must be improved before itcould be used in the drop test simulation.The main reason isthat in the long rod impact the compression force is localizedin a small area on the surface of the foam thus creating a com-bination of compression and shear. The material failure wassimulated with the aid of MAT ADD EROSION based onthe plastic strain and tensile stress [4]. Without introducingfailure in thematerialmodel, the crushable foamdeformationdue to the localized force shows problematic furrowing [4]and an unrealistic dent shape as shown in Figure 8. Thebrittle failure mode cannot be obtained without using anappropriate failure criterion.

The existing model was improved to avoid the negativevolume error which occurs due the large deformation inthe foam. To prevent this error, the stress strain curve wasextended exponentially at large strains [17]. The extendedcurve is shown in Figure 9. Also, one point integration solidelement was used with hourglass control type 2 [18]. To avoidmesh tangling in high compression areas, interior contact wasutilized with the activation thickness factor of 0.1. Contactinterior type 2 was activated to control a combined mode ofcompression and shear in LS-DYNA [4].

Allowing the foam elements to fail and erode causesanother problem. Some elements on the surface of foamwill erode and the projectile will come into contact withsome of the elements within the foam. Thus, surfaceto surface contacts are not recommended. To overcomethis problem, AUTOMATICE NODE TO SURFACE con-tact was used and a set of all the foam nodes was defined thatwere used in the contact command. However, this methodcarries a computational penalty.

By default, LS-DYNA removes the mass of the erodedelements to increase the stability of the calculation. However,the mass of the eroded elements must be considered as thereduction of mass might cause incorrect results. In CON-TROL CONTACT card, the value of ENMASS is changed tounity so that the mass of the eroding nodes is retained andcontinue to be active in contact [19].

5000

4500

4000

3500

3000

2500

2000

1500

1000

500

00 5 10 15 20 25 30 35 40 45

Forc

e (N

)

Displacement (mm)

ExperimentSimulation

Figure 7: Comparison between the experimental and simulationresults of the static compression test at 500mm/min.

4. Discussion

4.1. Quasi Static Compression Test. The compression testwas conducted to obtain the material properties of EPScrushable foams as well as to develop a preliminary materialmodel.Themost important required properties for modelingthe material are the density, stress strain curve, the elasticmodulus, and Poisson’s ratio. These properties were foundexperimentally. The elastic modulus and stress strain curvewere found to be dependent on the strain rate. As the strainrate increases, the elastic modulus increases and the stressstrain curve becomes stiffer. As for Poisson’s ratio, it wasfound to be independent of the strain rate and was alwaysequivalent to zero [12].

A Comparison between the experimental and simulationresults shows the capability of the model to reproduce thestress strain curve with acceptable accuracy as shown inFigure 7. Therefore, the suggested material parameters arecapable of accurately predicting the load and deformation ofEPS crushable foams.

However, it should be noted that even though the mate-rial model showed good accuracy in the compression testsimulation, it is still a preliminary model and needs to beimproved if it were to be used for large deformation andfailure simulations of EPS foam.

Failure due to shear or tension must be introduced inthe material model. Although crushable foams are not usedunder tension or shear loading, localized impact or thegeometry of the crushable foam might result in a combinedmode of shear, tension and compression [2].

4.2. Drop Test. The drop test experiment serves as an addi-tional verification of the suggested material parameters. The


Table 3: Input card for MAT CRUSHABLE FOAM.

Parameter Description Value UnitsMID Material ID numberRO Density 12.5 Kg/m3

𝐸 Young’s Modulus 0.0022 GPaPR Poisson’s ratio 0LCID Load curve ID for nominal stress versus strainTSC Tensile stress cut-off 0.1 × (10)−3 GPaDAMP Rate sensitivity via damping coefficient 0.5

Figure 8: Deformation of EPS foam without introducing failure criterion.

first problem encountered in the simulation was the negativevolume problem due to instability. The existing model canwithstand compression until only around 80 percent of itsoriginal length. This is because the stress strain curve usedin the model was obtained from the compression test inwhich the compression limit was 80 percent. However, in thedrop test experiment, due to the high kinetic energy of theprojectile, the crushable foam elements might be compressedmore than 80 percent of their original length. It may occurthat the strain in the simulation exceeds the last point of thestress-strain curve. If this happens, LS-DYNA extends thecurve linearly with last slope of the curve. This might lead torelatively small stress values and the negative volume problemmight occur.

The negative volume error problem was prevented byadopting two approaches. First, the stress strain curve wasexponentially extended at large strains as shown if Figure 9.This can be a very effective approach. Another importantparameter which greatly helps in preventing the negativevolume error is by introducing the “contact interior” in LS-DYNA. This type of contact was especially designed to beused for simulating soft materials. The contact interior type2 was activated, which was designed to control combinedmodes of compression and shear.

In the experiment, the brittle failure was observed inthe material due to shear loads. To simulate this modeof failure, ADD EROSION was utilized which allows theintroduction of failure criteria in the material model asMAT CRUSHABLE FOAM does not allow material erosion.The failure criteria defined was the maximum tensile stressand maximum plastic strain. The values of these criteriawere found by visual investigation and comparison betweenexperiment and the simulation. The points at which thematerial starts to crack and fail in the experiment were

identified, and the respective failure criteria values wereintroduced into simulation by trial and error method.

Comparing the projectile depth of penetration in theexperiment and simulation validates the developed materialparameters. As shown in Figure 10, the depth of penetrationprofile obtained in the simulation shows that the projectilereaches the maximum depth of penetration of 188 mmat 34 milliseconds. This value of the maximum depth ofpenetrationmatches the experimental average value as shownin Table 2. Also, the graph shows that the depth of penetrationslightly decreases after reaching the maximum depth ofpenetration then increases back to the maximum. This isinterpreted as the long rod projectile bouncing back slightlyafter reaching the maximum depth of penetration, whichwas actually observed in the experiment. Furthermore, visualcomparison between the physical testing and numericalsimulations shows the similarity in the failure mode of thecrushable foams. As depicted in Figure 11, the damage on thefoam was localized on the projected area of projectile and thefailure occurs due the shear strain.

5. Conclusions

Compression tests on EPS crushable foams were carried outat different strain rates.The effect of strain rate on thematerialproperties was established. It was found that at higher strainrates the material is able to withstand higher loads andabsorbs more energy. Moreover, elastic modulus and yieldstrength increments were found to be proportional to thestrain rate increase.

Compression test simulations were successfully per-formed and the results were validated by the experimentalwork.Thematerial model was capable to reproduce the stressstrain curve with acceptable accuracy.


0

0.5

1

1.5

2

2.5

3

0 20 40 60 80 100St

ress

(MPa

)Stain (%)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0 20 40 60 80 100

Stre

ss (M

Pa)

Strain (%)

Figure 9: Original (left) and extended (right) stress-strain curve.

0

0 20 40 60 80 100

Dep

th o

f pen

etra

ion

(mm

)

Time (ms)

−200

−180

−160

−140

−120

−100

−80

−60

−40

−20

Figure 10: Missile depth of penetration (simulation results).

Drop tests using long rod projectile impact against EPScrushable foam were conducted. The depth of penetrationwas recorded and the average value was calculated. Thefailure mode and the deformation in the specimen wereinvestigated. Numerical simulations were performed usingthe enhanced material parameters along with an appropriatefailure criterion that were able to reproduce the failuremodes observed during the experiments. Maximum depth of

Proj

ectil

e

Max

imum

shea

ring

strai

n

Com

pres

sed

mat

eria

l

Figure 11: Foam failure process in numerical analysis.

penetration obtained in LS-DYNA simulations agreed closelywith experimental work.

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper.


References

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[8] Q. Liu, G. Subhash, and X.-L. Gao, “A parametric study oncrushability of open-cell structural polymeric foams,” Journalof Porous Materials, vol. 12, no. 3, pp. 233–248, 2005.

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[11] M. Wronski, “A new hypoelastic model of the mechanicalbehaviour of polyurethane foams,” Computational MaterialsScience, vol. 5, no. 1-3, pp. 271–276, 1996.

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[14] V. I. Rizov, “Low velocity localized impact study of cellularfoams,” Materials and Design, vol. 28, no. 10, pp. 2632–2640,2007.

[15] P. A. Du Bois, S. Kolling, M. Koesters, and T. Frank, “Materialbehaviour of polymers under impact loading,” InternationalJournal of Impact Engineering, vol. 32, no. 5, pp. 725–740, 2006.

[16] LS-DYNATheoryManual Version, vol. 970, Livermore SoftwareTechnology.

[17] S. Bala, “Best practices for modeling recoverable low densityfoams-by example,” 2006, http://blog2.d3view.com/best-practices-for-modeling-recoverable-low-density-foams-by-ex-ample/.

[18] K. Weimar and J. Day, “Negative volumes in brick elements,”2003, http://www.dynasupport.com/howtos/element/negativ-volumes-in-brick-elements.

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Research Article Modeling Large Deformation and Failure of ...downloads.hindawi.com/journals/mse/2014/292647.pdf · LS-Dyna provides many material models for di erent types of foams